In this work, linear codes over the ring $\Cal S_4=\Bbb F_2+u\Bbb F_2+u^2\Bbb F_2+u^3\Bbb F_2$ are considered. The Lee weight and gray map for codes over $\Cal S_4$ are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and $(1+u^2$-constacyclic codes over $\Cal S_4$ are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over $\Cal S_4$.